std::numeric_limits::digits10

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std::numeric_limits
Static constants numeric_limits::is_specialized numeric_limits::is_signed numeric_limits::is_integer numeric_limits::is_exact numeric_limits::has_infinity numeric_limits::has_quiet_NaN numeric_limits::has_signaling_NaN numeric_limits::has_denorm numeric_limits::has_denorm_loss numeric_limits::round_style numeric_limits::is_iec559 numeric_limits::is_bounded numeric_limits::is_modulo numeric_limits::digits numeric_limits::digits10 numeric_limits::max_digits10 (C++11) numeric_limits::radix numeric_limits::min_exponent numeric_limits::min_exponent10 numeric_limits::max_exponent numeric_limits::max_exponent10 numeric_limits::traps numeric_limits::tinyness_before Static member functions numeric_limits::min numeric_limits::lowest (C++11) numeric_limits::max numeric_limits::epsilon numeric_limits::round_error numeric_limits::infinity numeric_limits::quiet_NaN numeric_limits::signaling_NaN numeric_limits::denorm_min Helper types float_round_style float_denorm_style

static const int digits10		(pre-C++11 version)
static constexpr int digits10		(C++11 version)

The value of std::numeric_limits<T>::digits10 is the number of base-10 digits that can be represented by the type T without change, that is, any number with this many decimal digits can be converted to a value of type T and back to decimal form, without change due to rounding or overflow. For base-radix types, it is the value of digits (digits-1 for floating-point types) multiplied by log
10(radix) and rounded down.

[edit] Standard specializations

T	value of std::numeric_limits<T>::digits10
/* non-specialized */	​0​
bool	​0​
char	std::numeric_limits<char>::digits * std::log10(2)
signed char	std::numeric_limits<signed char>::digits * std::log10(2)
unsigned char	std::numeric_limits<unsigned char>::digits * std::log10(2)
wchar_t	std::numeric_limits<wchar_t>::digits * std::log10(2)
char16_t	std::numeric_limits<char16_t>::digits * std::log10(2)
char32_t	std::numeric_limits<char32_t>::digits * std::log10(2)
short	std::numeric_limits<short>::digits * std::log10(2)
unsigned short	std::numeric_limits<signed short>::digits * std::log10(2)
int	std::numeric_limits<int>::digits * std::log10(2)
unsigned int	std::numeric_limits<signed int>::digits * std::log10(2)
long	std::numeric_limits<long>::digits * std::log10(2)
unsigned long	std::numeric_limits<unsigned long>::digits * std::log10(2)
long long	std::numeric_limits<long long>::digits * std::log10(2)
unsigned long long	std::numeric_limits<unsigned long long>::digits * std::log10(2)
float	FLT_DIG
double	DBL_DIG
long double	LDBL_DIG

[edit] Example

An 8-bit binary type can represent any two-digit decimal number exactly, but 3-digit decimal numbers 256..999 cannot be represented. The value of digits10 for an 8-bit type is 2 (8 * std::log10(2) is 2.41)

The standard 32-bit IEEE 754 floating-point type has a 24 bit fractional part (23 bits written, one implied), which may suggest that it can represent 7 digit decimals (24 * std::log10(2) is 7.22), but relative rounding errors are non-uniform and some floating-point values with 7 decimal digits do not survive conversion to 32-bit float and back. These rounding errors cannot exceed one bit in the representation, and digits10 is calculated as (24-1)*std::log10(2), which is 6.92. Rounding down results in the value 6.

This section is incomplete Reason: example of 7-digit decimal fraction that fails the roundtrip to float

[edit] See also

radix	the radix or integer base used by the representation of the given type (public static member constant)
digits	number of radix digits that can be represented without change (public static member constant)
min_exponent	one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant)
max_exponent	one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant)